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A Safe Zone Based Approach for
Monitoring Moving Skyline Queries
Computer Science and Engineering
Muhammad Aamir Cheema1, Xuemin Lin2,1, Wenjie Zhang1, Ying Zhang1
1The
University of New South Wales, Australia
2 East China Normal University
Introduction
k-Nearest Neighbors (kNN) Query
• Return k objects closest to the query point.
Skyline: A Multi-Criteria Query
• Given a set of criteria, an object A dominates another object B if A is
better than B for every criterion.
• Return every object that is not dominated by any other object.
Distance
Price
Rating
Distance
Price
Rating
5Km
$30
☺☺
20Km
$30
☺☺
Is distance the only criterian???
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Distance
Price
Rating
10Km
$20
☺☺☺☺
Introduction
Continuous Queries
• Continuously monitor the results as the query moves.
• E.g., Continuous kNN queries, continuous range queries, continuous
reverse k nearest neighbors queries
In this paper, we study continuous skyline queries for moving query points
where distance is one of the criterions.
Distance Price
Price
Distance
Rating
Rating
Distance
Price
Rating
5Km
15Km
3.1Km
☺☺
☺☺
20Km
15Km
4Km
$30
☺☺
$30
$30
We support arbitrary distance metric, e.g.,
Euclidean distance in 3d, road network distance
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Distance
Distance
5Km
10Km
3Km
Price
Price
$20
$20
Rating
Rating
☺☺☺☺
☺☺☺☺
Introduction
Solution Strategy
 Assign query a safe zone such that
 results remain valid as long as query remains inside the safe zone
 Re-compute the results only when query moves out of safe zone
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Related Work
Continuous Skyline Queries
 Huang et. al [TKDE 2006] and Lee et. al [ICDE 2009] (known velocities)
 Tian et. al [MOBIDE 2007] (moving objects, static query)
 Hsueh et. al [DEXA 2008] (designed for small update ratio)
Safe zone based approaches for other queries
 kNN queries: Zhang et. al [SIGMOD 2003], Nutanong et. al [PVLDB 2008] ,
Hasan et. al [SSTD 2009]
 Range queries: Zhang et. al [SIGMOD 2003] and Cheema et. al [ICDE 2010]
 Group NN queries: Li et. al [ICDE 2013]
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Solution Overview
Solution Strategy
 Compute safe zone and the query results
 results remain valid as long as query remains inside the safe zone
 Re-compute the safe zone and results when query moves out of safe zone
How to compute the safe zone?
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Formalizing Safe Zone
Ranking
An object A is a skyline object if and only if there does not exist any object X better
than A on every dimension, i.e.,
 An object A is a skyline if and only if, for each object X that is better than A in
every static dimension
 A is better than X in dynamic dimension (distance), i.e., A is closer to q than X
Static dimensions
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Price
Location coordinates
Formalizing Safe Zone
An
a skyline
long
as it does
is closer
q than
object
X
Anobject
objectAAremains
is a skyline
objectobject
if and as
only
if there
not to
exist
any every
objectsuch
X better
than

Impact
of an object
A on
everyregion
dimension,
i.e., A is the area such that A is a skyline object if and only if q
inside
this
areaX that is better than A in every static dimension
 isFor
each
object
Ranking
 A is better in dynamic dimension (distance), i.e., A is closer to q than X
An object A remains a skyline object as long as it is closer to q than every such object X
Static dimensions
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Price
Location coordinates
Formalizing Safe Zone
Ranking
An object A remains a skyline object as long as it is closer to q than every such object X
 Impact region of an object A is the area such that A is a skyline object if and only if q
is inside this area
Impact region of Y = Voronoi Cell of Y computed using Y and the objects that
are better than Y on every static dimension
Static dimensions
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E
Price
Location coordinates
Formalizing Safe Zone
Impact region of Y = Voronoi Cell of Y computed using Y and the objects that
are better than Y on every static dimension
 Y is a skyline object if and only if q is in the impact region of Y
 Note that result remains unchanged as long as q does not enter (or leave) an impact
region
 Safe Zone = IR(D) ∩ IR(C) ∩ IR(A) - IR(B) – IR(E)
IR(E)
Ranking
IR(D) = IR(C)
IR(B)
E
IR(A)
Static dimensions
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Price
Location coordinates
A Basic Algorithm
 Z = whole data space
 For each object o
 Compute impact region IR (o) of o
 If q is inside IR(o) // o is a skyline object
 Z = Z ∩ IR(o)
 Else
 Z = Z – IR(o)
Ranking
 Return Z
←
←
Static dimensions
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E
Price
Location coordinates
A Basic Algorithm
 Find the objects that are better than o in
every static dimension
 Compute Voronoi cell of o using o and
these objects
 Z = whole data space
 For each object o
 Compute IR (o)
 If q is inside IR(o) // o is a skyline object
 Z = Z ∩ IR(o)
 Else
 Z = Z – IR(o)
Ranking
 Return Z
Static dimensions
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E
Price
Location coordinates
Optimization: Pseudo-Impact Region
 Find the objects that are better than o in
 Z = whole data space
every static dimension
 For each object o
 Compute Voronoi cell of o using o and
 Compute IR (o)
these objects
 If q is inside IR(o) // o is a skyline object
 Z = Z ∩ IR(o)
 Find the skyline objects that are better than o
in every static dimension
 Compute Voronoi cell of o using o and these
objects
 Else
 Z = Z – IR(o)
Ranking
 Return Z
Static dimensions
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 Have to look only in the set of skyline
instead of the whole data set
 Voronoi cell computation becomes cheaper
(due to fewer objects)
Price
E
Location coordinates
Other optimizations: highlights
 Z = whole data space
 Prune un-necessary objects
 For each object o
 Compute IR (o)
 If q is inside IR(o) // o is a skyline object
 Z = Z ∩ IR(o)
 Else
 Z = Z – IR(o)
 Return Z
For Euclidean Space
 Extend pruning rules for R-tree
 Efficiently compute psuedo-impact regions using R-tree
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Experimental Settings
Dataset
– Real data set containing 175,813 POIs in North America
– Static attributes are synthetically generated
– Query points belong to cars moving on road network (using
Brinkhoff data generator)
100 queries are generated and each query is monitored for 5
minutes. Figures report the total cost for all queries.
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Experiments (effect of optimizations)
Basic: The basic algorithm
No-Pseudo: The optimization that uses psuedo-impact regions is not used
No-Pruning: The pruning rules are not used
Our: The optimization and pruning rules are applied
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Experiments (effect of data cardinality)
Supreme:
1. Compute skyline objects using BBS SIGMOD[2003] (an IO optimal
algorithm)
2. Compute safe zone using an oracle (zero cost)
3. Repeat 1 and 2 whenever query leaves the safe zone
Note: The IO cost of Supreme is the lower bound IO cost
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Experiments (effect of dimensionality)
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Experiments (effect of query speed)
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Thank You!
Any Questions?
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